NPV and IRR Explained: A Plain Guide with an Egyptian Worked Example

Net present value (NPV) and internal rate of return (IRR) appear in most serious feasibility studies and in the questions of most investors and partners, yet many small-business owners see them as formulas for specialists. Here is NPV and IRR explained in plain terms. The idea behind both is simple: a pound you will receive in five years is worth less than a pound in your hand today, so you cannot add up the next five years' profits as if they were cash now and compare them with what you pay today.

This article explains both measures in everyday language, shows how to choose a discount rate in Egypt using a documented interest rate and a published inflation figure, works through a full illustrative example step by step for a laundry, compares two investment options, and answers a practical question: when is the payback period enough on its own, and when do you need NPV?

Why adding up expected profits is not enough

Imagine two offers: the first gives you EGP 100,000 today, the second gives you EGP 100,000 in a year. You would take the first without thinking, because you could put the money in a bank and have more than EGP 100,000 a year from now, because prices rise so the same amount buys less next year, and because a promise of money in the future may not be kept. This is the "time value of money".

A small business is exactly this kind of decision: you pay a large amount today for equipment, fit-out and stock, in return for cash that comes in over several years. Calculating NPV is simply a time-value-of-money problem in which each cash flow is discounted back to its present value². The reason is that cash flows in different years cannot be added or compared directly; they must first be translated into a common time period².

Keep profit and cash apart here. The calculation uses each year's net cash flow, what actually comes in minus what actually goes out, not net profit from the income statement. Depreciation, for instance, is an expense on the income statement but no cash leaves, while the full price of equipment leaves as cash in the year you buy it. If this is not yet clear, start with our article on cash flow for small businesses and come back.

What is net present value (NPV)?

NPV is the difference between the present value of the cash inflows and the present value of the cash outflows². In everyday terms: what is everything the project will give you in the future worth today, after you subtract what you put into it?

The formula, step by step

For each year, divide the net cash flow by (1 + the discount rate) raised to the power of the year number. At a 25% discount rate, EGP 110,000 received in one year is worth 110,000 ÷ 1.25 = EGP 88,000 today, and EGP 170,000 received in two years is worth 170,000 ÷ (1.25 × 1.25) = EGP 108,800 today. Add up all these present values and subtract the amount invested today.

• Net cash flow: the cash that comes into the business in a year minus the cash that goes out, including taxes and replacements.
• Discount rate: the minimum yearly return you will accept for putting your money into this project rather than an alternative.
• Discount factor: the number you multiply each year's cash flow by, equal to 1 ÷ (1 + discount rate) raised to the year number. It gets smaller the further away the year is.

The decision rule

Projects with a positive NPV should be accepted, and projects with a negative NPV should be rejected². In practice, a positive figure means the project recovers your investment, earns the discount rate you chose on it, and leaves a surplus worth the NPV today. Zero means the project earns exactly the discount rate, no more and no less.

NPV has a clear advantage over the payback period, as it solves several of its problems²: it takes into account when each cash flow arrives, it counts every year rather than just the early ones, and it gives you the answer in pounds rather than in years.

What is the internal rate of return (IRR)?

IRR is the discount rate that sets the present value of the cash inflows equal to the present value of the cash outflows³, in other words the rate that makes NPV zero. To find it, set NPV to zero and solve for the discount rate³. There is no direct formula; it is found by trial: you try one rate after another until NPV reaches zero, which spreadsheet programs do for you automatically.

The decision rule: if the IRR is greater than the cost of capital, the project should be accepted³; if it is less, it should be rejected³. The cost of capital here is the same discount rate you use for NPV. That is why the two measures agree on accepting or rejecting a single project, as long as its cash flows are conventional (negative at the start, then positive), so if NPV is positive at 25%, the IRR is above 25%.

Why people like it, and why you should not rely on it alone

IRR's appeal is that it is a percentage that is easy to compare with an interest rate: "the project returns 32% and the bank pays 19%". But it has three limits you should know:

1. It can have more than one value. There may not be a single mathematical solution for IRR, which happens when negative cash flows occur in more than one period³, for example a project that needs a major equipment replacement in year four that makes that year's cash flow negative.
2. It assumes reinvestment at the same rate. IRR assumes the cash flows are reinvested at the IRR itself when they are received³, which may be unrealistic when the rate is very high.
3. It ignores size. It converts cash flows to a percentage and so ignores differences in the size of projects³. A 40% return for one year on EGP 50,000 is worth less than a 30% return for one year on EGP 500,000.

To deal with the reinvestment problem there is the modified internal rate of return (MIRR), in which cash flows are compounded at the cost of capital⁴. There is also the profitability index, which uses the same inputs as NPV but presents the result as a ratio⁴.

How to choose a discount rate for a business in Egypt

In theory, the right discount rate is the business's cost of attracting capital². A small-business owner rarely has a ready figure for that cost, so a practical method helps. Here is one in three steps.

Step 1: start from a documented interest rate

At its meeting on 24 September 2026, the Central Bank of Egypt kept the overnight deposit rate at 19%, the overnight lending rate at 20% and the main operation rate at 19.5%¹. The Monetary Policy Committee's next meeting is on 29 October 2026¹, so check the latest decision before you calculate. These figures give you a reference for the general level of returns in the economy: if you can earn something close to them at low risk in bank products, it makes no sense to accept less from a project that carries risk and effort.

Step 2: add a premium for your project's risk

Lenders charge a premium to higher-risk borrowers⁵, and the same logic applies to you as the investor in your own business. A new business in an activity you have never run, or one that depends on a single customer or on imported materials, deserves a bigger premium than an established business in a trade you know well. There is no official figure for this premium; it is your judgement, so show the result at more than one rate, as the example below does. If part of the project will be financed with a loan, the actual interest rate the bank or lender offers you is another floor the project's return must clear. But do not put the loan amount or its instalments into the cash flows you discount for NPV: the discount rate already reflects the cost of money, and including them counts the financing twice. Instalments belong in your cash plan.

Step 3: watch inflation

The quoted interest rate is the nominal rate; the real rate is the nominal rate minus the inflation rate⁵. Egypt's annual urban inflation was 13.9% in September 2026, after 14.5% in August⁶, and the Central Bank expects inflation to decline gradually towards its target of 7% (±2%) in the second half of 2027¹. By that formula, the real return on the overnight deposit rate is about 19% − 13.9% = 5.1%. That is an approximation; the more precise calculation is (1 + nominal rate) ÷ (1 + inflation) − 1, which, for illustration, gives about 4.48%, not 5.1%. The gap widens as rates rise: the real rate equivalent to a 25% nominal rate with 13.9% inflation is about 9.75%, not 11.1%. Use the inflation you expect over the project's life, not just last month's figure, especially since the Central Bank expects it to fall.

The practical rule is consistency. If you build your cash flows with prices that rise each year with inflation, use a nominal discount rate built from the reference interest rate plus your risk premium, such as the 25% in the example below. If you build them at today's fixed prices with no increases, use a lower, real rate. Mixing fixed-price cash flows with a high nominal discount rate is unfair to the project; the reverse flatters it.

Illustrative worked example: NPV and IRR for a laundry

This is an illustrative example. Its figures are assumed to explain the method and are not market prices. An owner is considering opening a laundry and ironing shop in a residential area:

• Investment today (year 0): EGP 600,000, of which EGP 420,000 is washing and ironing equipment, EGP 100,000 is shop fit-out and EGP 80,000 is working capital (supplies, detergents and operating cash).
• Yearly net cash flow after tax: EGP 110,000 in year one, then EGP 170,000, 210,000, 235,000 and 255,000 in years two to five as prices and customers grow.
• At the end of year five: the used equipment is sold for EGP 60,000 and the EGP 80,000 of working capital is recovered, so year five's cash flow is 255,000 + 60,000 + 80,000 = EGP 395,000.
• Discount rate: 25% a year: the 19% overnight deposit rate as a reference, plus a 6-point risk premium the owner chose because the trade is new to him. The 6-point premium is an assumption for this example, not a recommended figure, and many new businesses warrant more. The cash flows include rising prices, so a nominal rate is the right one.
• Horizon: five years, assuming the owner winds the business up at the end. If the business will keep running after year five, a cautious estimate of its continuing value can be added at the end, which would raise the NPV.

Total inflows over five years are EGP 1,120,000, almost twice the investment, and the undiscounted surplus is EGP 520,000. That looks reassuring, but it treats a pound in year five as if it were a pound today. Here is the proper calculation:

Reading the results

• NPV at 25%: the present values of years 1 to 5 add up to about EGP 530,010; after subtracting EGP 600,000, the NPV is negative by about EGP 69,990. Put differently: if you require 25% a year, this project does not deliver it.
• IRR: 20.21%. This is the yearly return implied by the project's cash flows: slightly above the 19% overnight deposit rate, but clearly below the 25% the owner requires for the risk.
• Simple payback: after three years EGP 110,000 is still unrecovered and year four brings EGP 235,000, so payback is 3 + (110,000 ÷ 235,000) = about 3.47 years, roughly three years and six months.
• Discounted payback: at 25% the project never recovers its discounted cost within the five years; the last column stays negative to the end.

This is what the two measures are for. An owner who looks only at payback sees "three and a half years, reasonable" and goes ahead, while the full calculation says the project barely beats an interest rate that carries none of the business's risk.

The NPV profile: how the answer changes with the discount rate

Because the discount rate is an estimate, it helps to build what is called an NPV profile: the NPV at a range of discount rates².

The point where NPV reaches zero is the IRR, 20.21%. The higher the discount rate, the lower the NPV, because the distant years, which hold the largest cash flows in this example, lose more of their value.

What would make the project acceptable at 25%?

• If every inflow in years 1 to 5 were 10% higher, including the recovered value at the end: NPV would be negative by about EGP 16,989 and IRR 23.86%. Still below the requirement.
• If all those inflows were 10% lower: NPV would fall to about EGP 122,991 negative and IRR to 16.36%, below the overnight deposit rate.
• A fixed yearly increase: the project needs about EGP 26,026 more net cash flow in each of the five years to bring NPV to zero at 25%.
• Or a smaller investment: the largest initial investment that makes the project acceptable at 25% with these same cash flows is about EGP 530,010, roughly EGP 69,990 less than the current plan. Good used equipment or a simpler fit-out might get there.

When NPV and IRR disagree: which option should you choose?

The two measures agree on accepting or rejecting a single project, but they can rank options differently. Mutually exclusive options are ones that compete with each other⁷: choosing one rules out the other, such as choosing between a small shop with a little equipment or a larger one with more equipment in the same location. The rule in this case is to take the option with the highest NPV⁷, and in the textbook's own example the option with the higher IRR was the one with the lower NPV⁷.

A second illustrative example at a 25% discount rate, with two options for the same shop over five years:

(Year five's cash flow in each option includes the recovered value of equipment and working capital: EGP 20,000 for the small option and EGP 50,000 for the large one.)

The small option wins on IRR and on payback, but the large option adds about EGP 24,486 more value. The reason is that the extra EGP 300,000 in the large option earns an IRR of 28.47% on its own, above the required 25%. If you have the extra money and no better use for it, the large option is the better choice under this rule. Note too that the choice depends on the discount rate: if the rate you require is above 28.47%, the small option has the higher NPV.

One caution: the rule assumes you can raise the larger amount. Managers often face a budget that limits how much they can invest in a given period⁷, and small-business owners face this more than anyone. If the large option needs a loan, put the instalments into your cash plan, not into the NPV cash flows, and make sure the larger risk is still acceptable to you.

Payback period: when it is enough and when it misleads

The payback period measures how long it takes a project to generate enough cash to recover its cost⁸. Its main advantage is its simplicity⁸, and the shorter it is, the greater the project's liquidity⁸. But it has two well-known flaws: it ignores the time value of money⁸, and it ignores cash flows after the payback point⁸. The discounted payback period fixes the first flaw by discounting cash flows at the cost of funds before counting the time⁴.

When payback alone is enough

• A small, short-lived investment, such as an extra machine that pays for itself in a few months, where discounting barely changes the picture.
• A quick first screen of many ideas, to rule out those that take many years to return the capital.
• When cash is the main constraint and your real question is: when do I get my money back to use elsewhere or repay a debt?

When you need NPV and IRR

• An investment that is large relative to your savings, or that runs for more than three years.
• High interest and inflation rates, as in Egypt now, because discounting at a high rate changes the value of distant years a great deal. In the example, simple payback was 3.47 years, discounted payback at 19% just before the end of year five, and at 25% it did not happen within five years.
• Choosing between two options that differ in size or timing.
• Presenting the project to a partner or investor who will ask about the return compared with their other options.

For monthly payback and how a gradual sales ramp-up changes it, see our article on break-even and working capital.

How to calculate NPV and IRR in Excel

You do not need to work out the factors by hand. Put the cash flows in one column in order, from year 0 to the last year, and use the NPV and IRR functions. Two details cause many errors:

1. Excel's NPV function starts at the end of the first period. According to Microsoft's documentation, the NPV investment begins one period before the date of the first value and ends with the last cash flow in the list⁹. So if the first cash flow happens at the beginning of the first period, meaning the investment you pay today, it must be added to the function's result, not included in its values⁹. In the laundry example: calculate NPV at 25% on the cash flows for years 1 to 5 only, then add -600,000. If you put the -600,000 inside the function, the program discounts it by a full year and gives you a wrong answer.
2. Excel's IRR function needs at least one negative and one positive value. The values must contain at least one positive value and one negative value¹⁰, and the cash flows must occur at regular intervals, such as monthly or annually¹⁰. The result is the rate that corresponds to a zero NPV¹⁰. If your cash flows fall on irregular dates, IRR is not suitable, since it requires regular intervals¹⁰. If the program cannot find a result after 20 tries, it returns the #NUM! error¹⁰; in that case try a different starting guess, since the default guess is 10%¹⁰.

If your cash flows are monthly, the IRR function gives you a monthly rate. Convert it to a yearly rate as (1 + monthly rate) to the power of 12, minus 1, not by multiplying by 12.

Common mistakes when calculating NPV and IRR

1. Discounting net profit instead of cash flow, so depreciation is treated as cash going out and the equipment cost disappears from the year of purchase.
2. Choosing a low discount rate because you want the answer to look good. The rate is chosen before the calculation, based on alternatives and risk, not after it.
3. Mixing fixed prices with a nominal rate, or inflated cash flows with a real rate.
4. Forgetting working capital at the start, and forgetting to recover it at the end.
5. Assuming full sales from year one, when a gradual ramp-up pushes the big cash flows into distant years that are discounted more.
6. Putting the investment inside Excel's NPV function, so it is discounted by a full year for no reason.
7. Relying on IRR alone to choose between two options of different sizes.
8. Ignoring equipment replacement midway through the project's life, which can make one year's cash flow negative and produce more than one IRR.
9. Projecting ten years or more for a small business, so the answer rests on distant figures nobody can trust. Five years is a reasonable horizon for most small businesses. But if you cut the calculation off at a given year and the business will carry on, add a cautious value for its continuation at the end or state plainly that you assume it is wound up, so you do not reject a good project.

Where NPV and IRR fit in your feasibility study

The two measures are not calculated in isolation; they come at the end of the chain of financial figures in the study:

• Start-up costs give you the year-0 cash flow. Review every item in our article on startup costs in Egypt.
• The projected income statement gives you profit, from which you move to cash by adding back depreciation and deducting capital purchases and the change in working capital. See our article on the income statement explained.
• The monthly and yearly cash flow is the direct input to the calculation.
• Scenarios: calculate NPV in the optimistic, realistic and pessimistic cases, not only the realistic one. A project that is positive in all three is far stronger than one that is positive only in the optimistic case.

If you are preparing the study for a lender, see what banks look for in our article on a feasibility study for a business loan in Egypt, and the full picture of what a study contains in our guide to feasibility studies in Egypt in 2026.

How Kleverz helps

Kleverz is an AI-powered platform for feasibility studies. If you are still at the idea stage, the free idea check takes about 5 minutes and gives you a verdict (proceed, adjust, validate first or avoid), a Kleverz Score out of 100 across five dimensions, the top 3 risks, and a first step to take in the next 48 hours.

If you want to see your business's numbers before you start, the detailed study is built on the numbers you enter: price, direct cost, expected volume, team, city and capital. It calculates start-up costs and fixed monthly costs including the employer's social-insurance share; a month-by-month cash flow for the first 12 months and a yearly summary over three years; monthly break-even revenue and the units needed per product or service; the operating break-even month, payback month, the deepest cash need and a recommended capital that adds a two-month reserve; optimistic, realistic and pessimistic scenarios; and the main risks, indicators to track and a week-by-week plan for the first month. It is delivered within 24 hours of payment confirmation, in Arabic or English. Its three-year yearly summary can be the starting point for your cash flows; you add your own assumptions for later years and the end value, then calculate NPV and IRR as shown here, at the discount rate you choose. When you decide to go ahead, Maher Consulting Firm, the human consulting arm, handles company formation.

Frequently asked questions

Sources

1. Akhbar El-Yom. 29 أكتوبر.. البنك المركزي يحسم مصير أسعار الفائدة على الإيداع والإقراض (in Arabic) (2026-10-19) — secondary source; Daily News Egypt. CBE lowers inflation forecasts, keeps key rates unchanged (2026-09-26) — secondary source. Checked 22 October 2026.
2. OpenStax. Principles of Finance 2e — 16.2 Net Present Value (NPV) Method (2026-06-24). Checked 22 October 2026.
3. OpenStax. Principles of Finance 2e — 16.3 Internal Rate of Return (IRR) Method (2026-06-24). Checked 22 October 2026.
4. OpenStax. Principles of Finance 2e — 16.4 Alternative Methods (2026-06-24). Checked 22 October 2026.
5. OpenStax. Principles of Finance 2e — 3.4 Interest Rates (2026-06-24). Checked 22 October 2026.
6. Daily News Egypt. Egypt's annual urban inflation eases to 13.9% in September (2026-10-10) — secondary source. Checked 22 October 2026.
7. OpenStax. Principles of Finance 2e — 16.5 Choosing between Projects (2026-06-24). Checked 22 October 2026.
8. OpenStax. Principles of Finance 2e — 16.1 Payback Period Method (2026-06-24). Checked 22 October 2026.
9. Microsoft Support. NPV function. Checked 22 October 2026.
10. Microsoft Support. IRR function. Checked 22 October 2026.